IMO 2014 Shortlist C5
Consider n ě 3 lines in the plane such that no two lines are parallel and no three have a common point. These lines divi...
Category: Combinatorics
Problem
Consider n ě 3 lines in the plane such that no two lines are parallel and no three have a common point. These lines divide the plane into polygonal regions; let F be the set of regions having finite area. Prove that it is possible to colour Pa n{2 T of the lines blue in such a way that no region in F has a completely blue boundary. (For a real number x, rxs denotes the least integer which is not smaller than x.) (Austria) Shortlisted problems 7